Skeleton structure inherent in discrete-time quantum walks

作     者：Yamagami, Tomoki Segawa, Etsuo Tanaka, Keńichiro Mihana, Takatomo Röhm, André Horisaki, Ryoichi Naruse, Makoto 

作者机构：Department of Information Physics and Computing Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo Tokyo113-8656 Japan Graduate School of Environment and Information Sciences Yokohama National University 79-1 Tokiwadai Hodogaya Kanagawa Yokohama240-8501 Japan Department of Mathematical Informatics Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo Tokyo113-8656 Japan 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Probability distributions 

摘      要：In this paper, we claim that a common underlying structure—a skeleton structure—is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the initial state, and partially, even of the coin matrix. This structure is best interpreted in the context of quantum-walk-replicating random walks (QWRWs), i.e., random walks that replicate the probability distribution of quantum walks, where this newly found structure acts as a simplified formula for the transition probability. Additionally, we construct a random walk whose transition probabilities are defined by the skeleton structure and demonstrate that the resultant properties of the walkers are similar to both the original QWs and QWRWs. Copyright © 2022, The Authors. All rights reserved.